Liveweaver's Paper On Expanding Confusion Is Confusing

arXiv:astro-ph/0310808v2 paper by Lineweaver dated 13 Nov 2003 entitled "Expanding Confusion: common misconceptions of cosmological horizons and the superluminal expansion of the universe" has a sentence in the second paragraph on page 4 that I find confusing.

The sentence is: "However, since the radius of the Hubble sphere increases with time, some photons that were initially in a superluminally receding region later find themselves in a subluminally receding region".

How can a photon that's in a region that's receding from us faster than c (in a universe where space is not only expanding but the rate of expansion is accelerating) find itself in a region that's traveling away from us at less than c?

The sentence preceding the one given above in Lineweaver's paper states: "Light that superluminally receding objects emit propagates towards us with a local peculiar velocity of c, but since the recession velocity at that distance is greater than c, the total velocity of the light is away from us".

arXiv:astro-ph/0310808v2 paper by Lineweaver dated 13 Nov 2003 entitled "Expanding Confusion: common misconceptions of cosmological horizons and the superluminal expansion of the universe" has a sentence in the second paragraph on page 4 that I find confusing.

The sentence is: "However, since the radius of the Hubble sphere increases with time, some photons that were initially in a superluminally receding region later find themselves in a subluminally receding region".

How can a photon that's in a region that's receding from us faster than c (in a universe where space is not only expanding but the rate of expansion is accelerating) find itself in a region that's traveling away from us at less than c?

Easy. The Hubble radius has itself been growing, and increasing typically at a rate faster than c

So if a photon is aimed at us, and is not too far out beyond the Hubble radius, and is not receding too fast, the Hubble radius can eventually extend out to it and include it.

The Hubble radius is the reciprocal of the Hubble parameter, so when the parameter decreases (as it has been doing for much of expansion history) the radius increases.

The Hubble radius is the radius of the sphere around us where the recession speed is NOT superluminal. So once a photon is inside that radius, it will eventually make it to us.

The sentence preceding the one given above in Lineweaver's paper states: "Light that superluminally receding objects emit propagates towards us with a local peculiar velocity of c, but since the recession velocity at that distance is greater than c, the total velocity of the light is away from us".

Aren't these two sentences contradictory?

Frank

No, not contradictory.
As I said, if the light is aimed at us, and not too far outside the Hubble sphere, then even though it starts out by, in effect, losing ground----seeming to be swept back, the Hubble sphere can expand to include it and then it is in a subluminal recession region----and it will make it here eventually.

The standard cosmo model----called LambdaCDM----is built into several available online calculators. A good way to get to know LCDM is to play around with the calculators. For example Morgan's calculator will show you what the Hubble parameter has been in the past (thousands of times larger than at present) and how rapidly it declined in earlier eras. Which means of course that the Hubble radius, its reciprocal, expanded at a fantastic rate (much more rapid than the expansion of spatial distance itself, in comparable distance range.)

Understanding this stuff is made remarkably easier if you spend some time with the online LCDM calculators which embody the standard model. Ned Wright's is also good.
I have a link to Morgan's cosmo calculator in my sig.

Photons are redshifted by expansion of the universe. This effectively permits them to also travel at superluminal velocities from the perspective of an observer 'outside' the universe. We would otherwise never observe a galaxy receeding at z>1.